**2. Process engineering characterisation**

The specific power input *P*/*V* is one of the central process engineering parameters. It describes how much power per volume is introduced into the bioreactor system. The power input influences various other parameters such as oxygen transfer, mixing intensity and fluid dynamic stress [21]. As already mentioned, a distinction can be made between mechanical, pneumatic, and hydraulic power inputs. Typical specific power inputs for microbial cultivations are >5 kW m�<sup>3</sup> [22] and thus significantly higher than for mammalian cells (5 to 310 W m�<sup>3</sup> ) [23, 24]. The specific power input, which is mechanically introduced into the bioreactor system can be determined by the torque *M* at a given stirrer speed *n* for volume *V* (eq. (1)).

$$P/V = \frac{2 \cdot \pi \cdot n \cdot M}{V} \tag{1}$$

The specific power input determined by this method corresponds to the average power input. The average power input is equal to the product of the average energy dissipation rate *ε* and the density *ρ* (eq. (2)) [9]. However, the energy dissipation rate in a bioreactor is not uniform and can differ by several orders of magnitude. For example, in a stirred bioreactor, the energy dissipation rate is maximum at the stirrer tips and decreases sharply as the distance from the tips increases. These differences in energy dissipation rate can be expressed in terms of hydrodynamic heterogeneity, which is the quotient of *ε*max and *ε*. Orbitally shaken systems are characterised by high homogeneity, where *ε*max/*ε* ranges from 1 to 18 [25, 26], and wave-mixed bioreactors lie between orbitally shaken and stirred bioreactors (8.8 to 32.0) [27]. The greatest heterogeneity can be observed in stirred bioreactors, with values of up to 66 for

*Computational Fluid Dynamics for Advanced Characterisation of Bioreactors Used… DOI: http://dx.doi.org/10.5772/intechopen.109848*

6-blade pitched turbines and as high as 147 for Rushton turbines [28]. Kolmogorov's microscale theory, which is often used as an indicator of possible cell damage, can be derived directly from the turbulent energy dissipation rate. Assuming isotropic turbulence, this theory states that eddies break down into smaller and smaller eddies and dissipate into heat at the Kolmogorov length *λk*. Eddies that are significantly larger than cells (e.g., 20 μm for CHO cells) damage the cells less and simply transport the cells with them. However, if the vortices are in the size range of the cells or smaller, this can lead to damage to the cell membrane. In addition to the Kolmogorov length, fluid dynamic stress can also be used to assess possible cell damage. This is composed of normal *σ* and shear *τ* stresses. Lethal and sublethal hydrodynamic stress varies greatly from one organism to another and can even vary for the same cell type [29]. In addition to the cell type, culture media composition [30, 31] and exposure duration also play crucial roles.

$$P/V = \frac{\sum(\varepsilon\_i)V\_i\rho}{V} = \overline{\varepsilon} \cdot \rho \tag{2}$$

The mixing time is another process engineering parameter which is of importance for large bioreactors. The mixing time corresponds to the time required to achieve a defined mixing quality *M* (typically 95% in biotechnology, eq. (3)). The mixing time should be kept as low as possible so that no oxygen and nutrient limitations or pH fluctuations occur. However, few exact values are published in the literature. For example, Anane et al. [32] showed that a clear metabolic switch occurred in a CHO cell line when the mixing time was longer than 90 s. However, the maximum mixing time suggested by Löffelholz et al. [33] for litre-scale devices is 30 s, which is below this critical value. A detailed description of the decolourisation method, which can be used to determine the mixing time, can be found in Bauer et al. [19] or in Maschke et al. [10].

$$M(t) = 1 - \frac{|c(t) - c\_{\infty}|}{c\_{\infty}} \tag{3}$$

A sufficient supply of oxygen is of critical importance in aerobic cultivations. In contrast to other nutrients, oxygen must be continuously added to the system, since it does not dissolve well in water-like media (Newtonian culture broths). The amount of oxygen required for a cultivation can be determined by the oxygen uptake rate (OUR), which is the product of the cell density and the specific oxygen uptake rate *qO*<sup>2</sup> . An overview of typical specific oxygen uptake rates can be found in Maschke et al. [10] and Seidel et al. [2]. To ensure sufficient oxygen supply, the oxygen transfer rate (OTR) must be equal to or greater than the OUR. The OTR is the product of the volumetric oxygen mass transfer coefficient *k*L*a* and the difference between the oxygen saturation concentration *C*<sup>∗</sup> and the dissolved oxygen concentration in the bulk liquid *C*.

For process characterisation purposes, the *k*L*a* value is of particular interest. This value is the product of the liquid side mass transfer coefficient *k*<sup>L</sup> and the specific interface *a*. In practice, the *k*L*a* value is typically determined directly. The most common methods are the gassing-out method, sulfite method and the respiratory gassing-out method, the latter of which is a biotic method. A detailed description of methods for determining the *k*L*a* value can be found in Seidel et al. [2] or Bauer et al. [19]. However, there are also measurement methods that allow the determination of just the specific interface (Section 4).

Another important parameter is the suspension criterion *N*S1. The characterisation of the sedimentation behaviour is particularly important for the cultivation of cells growing adherently on microcarriers, such as stem cells, which are also sensitive to hydrodynamic stress. Various authors have used the *N*S1 criterion to successfully grow stem cells on microcarriers [34–36]. This criterion describes the stirrer speed and thus the minimum power input required to completely suspend all microcarriers. It should be noted that at this speed only a suspension of the microcarriers is guaranteed, but not a homogeneous distribution in the cultivation vessel. This criterion ensures that not only are the cells subjected to the minimum necessary hydrodynamic stress, but also that there is no nutrient limitation due to heap formation. The *N*S1 criterion can be determined using a camera without the need for extensive apparatus.
